I've done the search, checked the FAQ, and checked the manual, but nowhere does it explain what actual difference there is if you crank up the AI difficulty level for each nation from normal to hard etc. Does the AI get more resources, other bonuses, become smarter?
It gets more design points, and at higher levels, more gold and gem income, resources and supplies. It might also get better at research, but that might just be because it can raise the Magic scale with those extra points.